While filing faxes separately from your wife would have been a problem were either of you applying for a marriage-based green card, that is no problem whatsoever when applying for citizenship, as long a "married, filing separately". In other words, if you admit to IRS that you are married but choose to (for tax purposes) to file separately.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
Continuing from atty Behar's answer with which I agree ... if, on the other hand, you and your wife have filed as "single" (that is, unmarried), then your taxes are improperly filed. This will have two problems. First, toward good moral character, you are not filing your taxes properly and maybe not honestly. Second, if your green card was based on your marriage, it may cast some doubt on whether your green card was properly awarded in the first place - that is, it may cause USCIS to wonder if you had a valid marriage. An AVVO responded last week had a roommate whose 5-year N-400 was denied and is expecting to be put in proceedings because his green card was based on a fraudulent marriage. USCIS saw signs of this in his N-400 filing, investigated, and concluded it had made a mistake previously.
If your taxes are "Married, Filing Separately" you have no problem. If they are not, amend them. If your marriage was valid but suspicious, get a lawyer to help you prepare your N400
Andrew M. Bramante, Rosner Partners, 216-771-5588. Free telephone consultation. You should always consult with an experienced immigration attorney to make certain that the advice you received is appropriate for your particular immigration case.
This will be a problem if your filed as "single." I suggest that you amend your return to the "married filing separately" status prior to applying for citizenship. Although you are not applying for citizenship based on your marriage to a US citizen, this is still relevant given that you are required to file taxes and be truthful when doing so.